Practical Considerations and Limitations of Using Leaf and Canopy Temperature Measurements as a Stomatal Conductance Proxy: Sensitivity across Environmental Conditions, Scale, and Sample Size

Stomatal conductance (gs) is a crucial component of plant physiology, as it links plant productivity and water loss through transpiration. Estimating gs indirectly through leaf temperature (Tl) measurement is common for reducing the high labor cost associated with direct gs measurement. However, the relationship between observed Tl and gs can be notably affected by local environmental conditions, canopy structure, measurement scale, sample size, and gs itself. To better understand and quantify the variation in the relationship between Tl measurements to gs, this study analyzed the sensitivity of Tl to gs using a high-resolution three-dimensional model that resolves interactions between microclimate and canopy structure. The model was used to simulate the sensitivity of Tl to gs across different environmental conditions, aggregation scales (point measurement, infrared thermometer, and thermographic image), and sample sizes. Results showed that leaf-level sensitivity of Tl to gs was highest under conditions of high net radiation flux, high vapor pressure deficit, and low boundary layer conductance. The study findings also highlighted the trade-off between measurement scale and sample size to maximize sensitivity. Smaller scale measurements (e.g., thermocouple) provided maximal sensitivity because they allow for exclusion of shaded leaves and the ground, which have low sensitivity. However, large sample sizes (up to 50 to 75) may be needed to differentiate genotypes. Larger-scale measurements (e.g., thermal camera) reduced sample size requirements but include low-sensitivity elements in the measurement. This work provides a means of estimating leaf-level sensitivity and offers quantitative guidance for balancing scale and sample size issues.

The surface energy balance is a budget of energy fluxes crossing a control surface.Considering fluxes of radiation, sensible heat, and latent heat from both sides of a leaf leads to the leaf energy balance equation [23], which can be solved iteratively for the leaf surface temperature The absorbed all-wave radiation flux R consists of absorbed incoming shortwave (R SW ) and long wave radiation (R LW ) fluxes.Incoming long wave radiation was estimated as follows where " g is the emissivity of the ground (assumed equal to 1), T g is the ground temperature, calculated by the ground energy balance equation (described below)." s is the e↵ective emissivity of the sky and was calculated according to [54] as where p (cm of precipitable water) is the atmospheric water vapor path length estimated according to [55].The above formulation of R LW stated in Eq.S2 e↵ectively assumes that the leaf is isolated in space, and thus receives half of its long wave radiation from the ground, and the other half from the sky.For more realistic plant geometries (i.e., that of the case study), the R LW was calculated using a 3D radiative transfer model (see below).
The leaf boundary layer conductance to heat was calculated using the Polhausen Equation (Eq.S4) where U (m s 1 ) is the wind speed outside the leaf boundary layer, assumed to be perpendicular to the leaf surface, L (m) is the characteristic dimension, which in this case corresponds to the width across the widest part of a patch or leaf.The factor of 2 accounts for convective heat transfer from both surfaces of the leaf, which is symmetric for both sides under the assumption of fully forced convection.
The semi-mechanistic model of [56] was used to estimate the stomatal conductance, which was calculated as where Q is the photon flux density (µmol/m 2 s), E m is the maximum transpiration rate at high VPD, i o relates to nocturnal transpiration, k and b are empirical parameters relating to leaf-specific hydraulic conductance and turgor to conductance scalar.
The boundary layer conductance to moisture g M consists of two serial pathways for water vapor transport from the leaf: one across the stomatal pore (associated with the stomatal conductance g s ), and another across the leaf boundary layer (associated with the boundary layer conductance to water vapor 1.08g H ). The boundary layer conductance to moisture was estimated to be 1.08 times that of the boundary layer conductance to heat, according to the approximate ratio of di↵usivity of water vapor to heat in the air.By combining the two conductances in series, and assuming that stomata are primarily located on the lower leaf surface, the overall conductance to water vapor is Equation S1 was iteratively solved for the leaf temperature T l using the secant method [57].For each set of ambient conditions, g s was varied from 0 and 1 mol m 2 s 1 and the resulting surface temperature was computed and fitted to Eq. 2 to derive the value of c, where T dry and T wet are the leaf surface temperatures when g s is 0 and 1 mol m 2 s 1 , respectively.
The above methodology was used for the calculation of leaf surface temperature and was adapted to estimate ground temperature (T g ) and the temperatures of non-leaf plant components (e.g., panicle, stem) considered in the subsequent case study.Notably, the ground is treated as a one-sided surface, meaning it emits and absorbs radiation on one surface, therefore the net radiation flux (left-hand side of Equation S1) becomes R T 4 g , where T g is the ground temperature.In addition, the ground boundary layer conductance was calculated as [58] g H = 0.166 + 0.5U.
SW (W m 2 ) is the absorbed shortwave/solar radiation flux, R LW (W m 2 ) is the absorbed longwave/terrestrial radiation flux, is the Stefan-Boltzmann constant (5.67 ⇥ 10 8 W m 2 K 4 ).c p is the heat capacity of air (25.95J mol 1 K 1 ), g H (mol m 2 s 1 ) is the boundary layer conductance to heat from the surface to the outside of the boundary layer, T air is the absolute temperature of the air immediately outside of the leaf boundary layer, and Rh is the air relative humidity immediately outside of the leaf boundary layer.is the latent heat of vaporization of air (44, 000 J mol 1 ), g M (mol m 2 s 1 ) is the conductance to water vapor between the leaf sub-stomatal cavity and outside of the leaf boundary layer.e l (P a) and e a (P a) are the air saturation vapor pressures evaluated at the leaf and air temperature, respectively, which were calculated using the Tetens equation [23].P atm (P a) is the atmospheric pressure (101, 000 P a).The term e l eaRh Patm represents the VPD, and the product of the VPD and g M is the transpiration rate.

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Figure S1: A linear fit showing simulated and predicted values of S-parameters with corresponding R 2 values.Overall, the R 2 values were greater than 0.97 for all scenarios, which shows that the equations have a good prediction.To develop mathematical models for S-parameters, the Helios framework was used to generate T l values for variations in g s (0 1 mol m 2 s 1 ), T air (10 40 C), Rh (0.2 0.8), and U (1 5 m s 1 ) for both sunlit and shaded leaves.These T l and g s values were plotted to generate Fig.1, and the curve was fitted to Eq.2 to obtain S-parameter values (c, T wet , and T ) for each combination of ambient conditions.Considering one S-parameter at a time, data

Figure S3 :
Figure S3: Comparing leaf temperature and sensitivity responses to stomatal conductance across five genotypes under various viewing angles and environmental conditions for (a-e) Infrared thermometer and (f-j) Thermocouple.

Table S2 :
Summary of field measurements used to develop the sorghum 3D structures in Helios.A stem radius of 0.011 m was used for all genotypes.